A stone is dropped from a height \(h\). It hits the ground with a certain momentum \(p\). If the same stone is dropped from a height \(100\)% more than the previous height, the momentum when it hits the ground will change by:
1. \(41\)%
2. \(200\)%
3. \(100\)%
4. \(68\)%
A particle of mass \(M\) starting from rest undergoes uniform acceleration. If the speed acquired in time \(T\) is \(V\), the power delivered to the particle is:
1. \(\frac{1}{2}\frac{MV^2}{T^2}\)
2. \(\frac{MV^2}{T^2}\)
3. \(\frac{1}{2}\frac{MV^2}{T}\)
4. \(\frac{MV^2}{T}\)
A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude \(P_0\). The instantaneous velocity of this car is proportional to:
1. \(t^{\frac{1}{2}}\)
2. \(t^{\frac{-1}{2}}\)
3. \(\frac{t}{\sqrt{m}}\)
4. \(t^2 P_0\)
A mass \(m\) moving horizontally (along the x-axis) with velocity \(v\) collides and sticks to a mass of \(3m\) moving vertically upward (along the y-axis) with velocity \(2v.\) The final velocity of the combination is:
1. \(\dfrac{3}{2}v\hat{i}+\dfrac{1}{4}v\hat{j}\)
2. \(\dfrac{1}{4}v\hat{i}+\dfrac{3}{2}v\hat{j}\)
3. \(\dfrac{1}{3}v\hat{i}+\dfrac{2}{3}v\hat{j}\)
4. \(\dfrac{2}{3}v\hat{i}+\dfrac{1}{3}v\hat{j}\)
\(300 ~\text{J}\) of work is done in sliding a \(2~\text{kg}\) block up an inclined plane of height \(10~\text{m}\). Taking \(g=\) \(10\) m/s2, work done against friction is:
1. \(200 ~\text{J}\)
2. \(100 ~\text{J}\)
3. \(\text{zero}\)
4. \(1000 ~\text{J}\)
A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation s = t2, where t is in sec. Work done by the force in 2 sec is:
1.
2.
3.
4.
The potential energy of a long spring when stretched by \(2\) cm is \(U\). If the spring is stretched by \(8\) cm, the potential energy stored in it is:
1. \(4U\)
2. \(8U\)
3. \(16U\)
4. \(U/4\)
A vertical spring with a force constant \(k\) is fixed on a table. A ball of mass \(m\) at a height \(h\) above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance \(d\). The net work done in the process is:
1. \(mg(h+d)+\frac{1}{2}kd^2\)
2. \(mg(h+d)-\frac{1}{2}kd^2\)
3. \(mg(h-d)-\frac{1}{2}kd^2\)
4. \(mg(h-d)+\frac{1}{2}kd^2\)